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Some Interesting Times:

Table of Contents:

NOTE: Due to typographical limitations ofHTML, sometimes } denotes greater than, { less than, and k theLaplacian.

Hot Ordinary Matter: Times of Transitions

At T = 10^19 GeV, Planck Energy. At T = 10^16 GeV, SU(5) GUT Monopole formation ends                   and the Inflationary Higgs mechanism eliminates                   the relic Monopoles. At T = 10^14 GeV, Zizzi Reheating and SU(5) Unification ends.  
The phase transition at the end of inflation atabout 10^15 GeV or about 10^(-34) sec sees (at 10^14 GeV) the GUT SU(5) is broken to SU(3)xU(2).In The Early Universe (paperback edition Addison-Wesley 1994) Kolb and Turner say (at p. 526):"... SU(5) GUT ... Additional Higgs bosons are required the very least one complex 5-dimensional Higgs.The 5-dimensional Higgs containsthe usual doublet Higgs required for SSB adna color triplet Higgs ... which can alsomediate B,L [baryon,lepton] violation.The triplet component must acquire a mass comparableto ... M = 3 x 10^14 GeV ... to guarantee the proton's longevity,whilethe doublet component must acquire a mass of order of a few 100 GeVto trigger electroweak SSB at the appropriate scale. ...".   That indicates to me that the GUT phase transitionat 10^(-34) sec does not produce electrons and protons withthe customary 0.5 MeV and 1 GeV masses that we now see,but rather produces massive composite GUT monopoles   with mass at 10^17 GeV, and consequentlywith Compton radii least about 100 Planck lengths,or 10^(-31) cm, and therefore of Compton vortex volume 10^(-93) cm,so that 10^80 of them would have volume 10^(-13) cm^3, much smaller than the 1,000 cm^3 volume of our universe at 10^(-34) sec with size 10 cm.   It is only later, at the electroweak phase transitionof about 100 GeV at whichthe electroweak U(2) is broken to U(1)xSU(2)with the SU(2) weak bosons becoming massiveand the leptons and quarks getting their individualmasses from the electroweak Higgs Yukawa couplingthat uses the "usual doublet Higgs" described by Kolb and Turner.
At T = 100 GeV = 10^15 degK the Higgs mechanism has been effective, the SU(2) weak force symmetry breaking has occurred, and the energy level is on the order of the Truth Quark mass of 130 GeV. 
Above the electroweak transition scale of about 100 GeV, at the time of about 10^(-11) sec after the big bang, when the size of the universe is about 10 x 10^(15-2) = 10^14 cm orabout 10^(14-18) = 10^(-4) light years,the Higgs mechanism has not taken effect, so that there is no Higgs Yukawa coupling to give mass to leptons and quarks, so that leptons and quarks are then massless,so their compton radius is not definedand electrons are no more confined to any particular spatial volume than are individual photons in our present universe.   The D4-D5-E6-E7-E8 VoDou Physics model has    Compton Radius Vortex electrons,and electrons have Compton radius about 10^(-11) cm.   10^80 electrons of that size would requirea volume of about 10^80 x 10^(-33) = 10^47 cm^3which isa size of about 10^16 cm or about 10^(-2) light yearswhich is greater thanthe 10^(-4) light year size of the universe at the timeof the electroweak/Higgs phase transition.   However, the ambient temperature of the universe is then about 100 GeV, andthe electron has second and third gneration counterparts,the muon of mass about 100 MeVandthe tauon of mass about 2 GeV,whichare effectively excited states into which the electron willbe kicked by the high 300 GeV temperature of the ambient universe.   That means thatany set of 10^80 electrons that found themselves inthe 300 GeV universe at the time 10^(-11) secwould immediately be transfomed into muons and tauons.   If all 10^80 of them were muons,then, since 100 MeV muons have a Compton radius of about 10^(-13) cm,   10^80 muons, each with volume 10(-39) cm^3,would fit into a volume of 10^(80-39) = 10^41 cm^3,or of size 10^14 cm,which isthe size of the universe at the 300 GeV electroweak phase transition.   It is an interesting coincidence (which I realized during a March 2001 series of e-mail conversations with Jack Sarfatti) that the electroweak phase transition occurs just when the 10^80 muon Compton Radius Vortices could fit into our universe.The size required for tauons, only an order of magnitude smaller, is still pretty close to the volume of our universe at the time of the electroweak phase transition.
 Farrar and Shaposhnikov have suggested that first order phase transition processes at this stage might account for particle-antiparticle asymmetry,butHuet and Sather, and Gavela, Hernandez, Orloff, and Pene say that QCD damping effects in bubble walls would reduce the asymmetry to a negligible amount.However,Nasser and Turok point out that when such other processes as formation of longitudinal Z condensate are taken into accountthe observed asymmetry might indeed be produced,and Farrar and Shaposhnikov havereplied to Gavela et. al. and Huet et. al., stating that the Gavela-Huet calculational scheme violates unitarity and is unreliable.   A nice overview is Farrar's 1994 invited talk at Stockholm. 

In hep-ph/0008142,Ayala and Pallares say "... the three well know Sakharovconditions ... (1) Existence of interactions that violate baryonnumber; (2) C and CP violation; (3) departure from thermalequilibrium ... are met in the standard model (SM) ofelectroweak interactions if the electroweak phase transition (EWPT)is of first order ... the EWPT turns out to be only too weakly firstorder which in turn implies that any baryon asymmetry generatedat the phase transition was erased by the same mechanism thatproduced it, i.e. sphaleron induced transitions ... Moreover, theamount of CP violation coming from the CKM matrix alone cannotaccount by itself for the observed asymmetry, given that its effectshows up in the coupling of the Higgs with fermions at a highperturbative order ... giving rise to a baryon to entropy ratio atleast ten orders of magnitude smaller than the observed one.Nevertheless, it has been recently pointed out that,provided enough CP violation exists, the above scenario couldsignificantly change in the presence of large scale primordialmagnetic fields ... which can be responsible for a stronger firstorder EWPT. The situation is similar to a type I superconductorwhere the presence of an external magnetic field modifies the natureof the superconducting phase transition due to the Meissnereffect. ... Recall that for temperatures above the EWPT, theSU(2) x U(1)y symmetry is restored and the propagating, non-screenedvector modes that represent a magnetic field correspond to the U(1)yhypercharge group. Thus, in the unbroken phase, any primordialmagnetic fields belong to the hypercharge group instead of to theU(1)em group and are therefore properly called hypermagnetic fields.... we show that the existence of such primordial hypermagneticfields also provides a mechanism to produce a large enough amount ofCP violation during the EWPT to possibly explain the observed baryonto entropy ratio in the SM. This can happen during the reflectionof fermions off the true vacuum bubbles nucleated during the phasetransition through an interference process equivalent to theBohm-Aharanov effect, given that in the unbroken phase, fermionscouple chirally to hypermagnetic fields with the hypercharge. Thechiral nature of this coupling implies that it is possible to build aCP violating asymmetry dissociated from non-conserving baryon numberprocesses that can then be converted to baryon number in the unbrokenphase where sphaleron induced transitions are taking place with alarge rate. The existence of such asymmetry provides a bias forbaryon over antibaryon production. ... We estimate that for stronghypermagnetic fields By = ( 0.3 - 0.5 ) T^2 the baryon to entropyratio can be RHO_B / S = ( 3 - 6 ) x 10^(-11) for slowly expandingbubble walls. ...".

In hep-ph/0208152Massimo Giovanni says: "... In cosmology the possible existence ofmagnetic fields prior to decoupling can influence virtually all themoments in the thermodynamical history of the Universe. Big-bangnucleosynthesis (BBN), electroweak phasetransition (EWPT), decoupling time are allinfluenced by the existence of magnetic fields at the correspondingepochs. ... The physical picture we have in mind is ... thefollowing. Suppose that conformal invariance is broken at some stagein the evolution of the Universe, for instance thanks to the(effective) time variation of gauge couplings. Then, vacuumfluctuations will go outside the horizon and will be amplified. Theamplified magnetic inhomogeneities will re-enter (crossing thehorizon a second time) during different moments of the life of theUniverse and, in particular, even before the BBN epoch. ... If thehypermagnetic flux lines have a trivial topology they can have animpact on the phase diagram of the electroweak phase transition ...If the topology of hypermagnetic fields is non trivial, hypermagneticknots can be formed .... and, under specific conditions, the BAU canbe generated ... A classical hypermagnetic background in thesymmetric phase of the EW theory can produce interesting amountsof gravitational radiation in afrequency range between 10^(-4) Hz and the kHz. ... For thehypermagnetic background required in order to seed the BAU theamplitude of the obtained GW can be even six orders of magnitudelarger than the inflationary predictions. ...

... if hypermagnetic fields are present at the EW epoch,matter-antimatter fluctuations are likely to be produced at BBN.... the success of BBN can be used in order to bound the magneticenergy density possibly present at the time of formation of lightnuclei. ...

... Before decoupling photons, baryons andelectrons form a unique fluid which possesses only monopole anddipole moments, but not quadrupole. ... Large scale magnetic fieldspresent at the decoupling epoch can have various consequences. Forinstance they can induce fluctuations in the CMB ... they can distortthe Planckian spectrum of CMB ... they can distort the acoustic peaksof CMB anisotropies ... and they can also depolarize CMB ...".

 From T about 5 GeV to T = 100 MeV = 10^12 degKthe energy level goes down through the masses of the 5 lighter quarks, and down to the mass of the fundamental composite hadrons, the protons and pions.  There is an SU(3) color force QCD phase transition from quark-gluon plasma to a hadronic gas.  
Above the quark-hadron transition scale of about 100 MeV,where the size of the universe is about 10 x 10^(18-2) = 10^17 cm orabout 10^(17-18) = 10^(-1) light years,there are no individual protons or other hadrons,and there is only a soup of quarks and leptons.
 Michael Hawkins, in his book Hunting Down the Universe (Little, Brown 1997) proposes that the QCD phase transition may be first order and so may produce density fluctuations that could create Jupiter-mass black holes.  Hawkins says that David Schramm has argued that such Jupiter-mass black holes would form in catastrophic collapse around Truth Quarks, whose mass is substantially greater than the energy level of the QCD phase transition.   Such Jupiter-mass black holes might be observed as gravitational microlenses that appear in every line of sight to distant quasars.  They would be about the size of beach balls, would be so massive that their decay time from Hawking radiation would be about 10^57 years, and would be uniformly distributed in the universe.  If all the small black holes were consolidated into the Jupiter-mass ones, and if there were enough of them to  give our universe its critical mass, there would be about one every 30 light years or so.  If our universe has less than critical mass, there would be fewer of them.  Jedamzik has proposed that similar black holes could be formed during the later part of the QCD phase transition, when the QCD-horizon mass scale would be about one solar mass, and that such black holes might constitute the dark matter of of galactic haloes. In this case, the black holes would not be uniformly distributed throughout the universe, but would be concentrated near galaxies.  However, it is my opinion that there is no requirement for the existence of galactic halo dark matter, because galactic rotation curves can be accounted for by MOND-Segal conformal gravitation. Therefore, I think that, although Jedamzik's mechanism for creation of black holes may be correct, I do not agree with his idea that they account for galactic halo dark matter (as opposed to cosmological dark matter).  Another possibility for at least some dark matter is gravitational interaction from other Worlds of the Many-Worlds.  From T = 1 MeV = 10^9 degK down to about T = 0.1 MeV, nucleosynthesis occurs.  Neutrinos decouple before T drops below the electron mass 0.51 Mev,so that electron-positron annihilation entropy goes to photons and not to neutrinos.

According to astro-ph/0302431,by Cyburt, Fields, and Oliver: "... Big bang nucleosynthesis...[(BBN)]... has long provided the primary determination ofthe cosmic baryon density OMEGA_B h^2, or equivalently thebaryon-to-photon ratio n ... = n_10 / 10^10 ... With theprecision of WMAP, the CMB nowoffers a significantly stronger constraint on n ... shown in thevertical (yellow) band ...

... the CMB ... strongly suggest[s]... that the D/Hmeasurements are accurate, while both the 4He and 7Li abundancesare systematically small. ... Primordial light element abundancesas predicted by BBN and WMAP ... the dark shaded distributions ...and ... the observational abundances (... the lighter shadeddistributions) ... are shown ...


According to astro-ph/0307213,by Cuoco, Iocco, Mangano, Miele, Pisanti, and Serpico: "...Theoretical estimates for nuclei abundances, along with thecorresponding uncertainties, are evaluated using a new numericalcode, where all nuclear rates usually considered have been updatedusing the most recent available data. Moreover, additional processes,neglected in previous calculations, have been included.... using theWMAP result ... at N_eff = 3.04... we get

we report in parenthesis the experimental value or the bestestimate currently available: ...

... There are two different ... primordial abundance ...determinations of Y_p: Y_p = 0.234 +/- 0.003 ... and Y_p = 0.244 +/-0.002 ... If the statistical error were not underestimated, this twovalues would be only marginally compatible. ... even the higher valueof Y_p ... appears in slight disagrement (1.6 sigma effect) withstandard BBN. .. Concerning 7Li experimental measurements ... theprimordial origin of the Spite plateau has been recently questioned.In particular ...[there was found]... evidence for adependence of X_7Li on metallicity. ... the discrepancy between themost recent observations ... and our theoretical value is now reducedto a less than 3 sigma effect. The average over the differentobserved values for X_7Li ... which are mutually compatible, givesX_7Li = 2.04 +/- 0.07. ...".

According to Two World Systems Revisited: A Comparison of PlasmaCosmology and the Big Bang, by Eric J. Lerner, author ofThe Big Bang Never Happened, Viking Press, New York, 1992:"... The dominant theory of cosmology, the Big Bang, is contradictedby observation, and has been for some time. The theory's predictionsof light element abundance, large-scale structure, the age of theuniverse and the cosmic background radiation (CBR) are in clearcontradiction with massive observational evidence, using almost anystandard criteria for scientific validity. This situation is not new.In 1992, I reviewed these contradictions ... and concluded thattheory had already been clearly falsified. Since that time, theevidence against the Big Bang has only strengthened. There is asecond framework for cosmology--plasma cosmology. This approach,which assumes no origin in time for the universe and no hot,ultradense phase of universal evolution, uses the known laws ofelectromagnetism and the phenomena of plasma behavior to explain themain features of the universe. ...

... In contrast to the extremely bad performance of BBN[Big Bang Nucleosynthesis], the predictions of the plasmaalternative have held up remarkably well. Plasma filamentation theoryallows the prediction of the mass of condensed objects formed as afunction of density. This leads to predictions of the formation oflarge numbers of intermediate mass stars during the formations ofgalaxies ... These stars produce and emit to the environment largeamounts of 4He, but very little C, N and O. In addition cosmic raysfrom these stars can produce by collisions with ambient H and He theobserved amounts of D and 7Li. The plasma calculations, whichcontained no free variables, lead to a broader range of predictedabundances than does BBN, because the plasma theory hypothesizes aprocess occurring in individual galaxies, so some variation is to beexpected.

... the ... observations that no galaxies, indeed no stars,have been observed that are entirely free of heavier elements...[are]... in accord with the predictions of theplasma-based stellar production of light elements. ...

The most dramatic confirmation of the predictions of theplasma-stellar model is in the discovery of large number of whitedwarfs in the halo of the Milky Way. Since the theory predictsthe formation of an initial population of intermediate-mass stars, itis a straightforward deduction that these stars must leave behindwhite dwarfs that should exist at present. Specifically the theorypredicts that somewhat less than half the total mass of the galaxyshould exist in the form of collapsed cores-either white dwarfs orneutron stars ... and for the intermediate stars, which are too smallto become supernovae, the normal end-point would be white dwarfs.Recent observations of high proper motion stars have shown that halowhite dwarfs constitute a mass of about 10^11 solar masses,comparable to about half the total estimated mass of the Galaxy ...While these observations have been sharply criticized, they have beenconfirmed by new observations ... Not only are the existence of thesenumerous white dwarfs confirmation of much earlier predictions by theplasma theory, they create new and insurmountable problems for BBN.Even if the progenitor stars were only 2-3M, a mass of He equal toabout 10-15% of the mass of the remnant white dwarfs would bereleased into the ISM. This would account for at minimum 50% of theobserved He abundance, reducing the possible contribution from theBig Bang to less than 12% of the total mass. Such a low production of4He is impossible with BBN for a baryon/photon ratio even as low as 1x 10^(-10). Thus the plasma model has successful predicted a newphenomenon, while the BBN model has been decisively contradicted byobservation. ...

 The large scale structure of the universe is inhomogeneousat all scales that have been observed ... In particular, galaxiesare organized into filaments and walls that surround largevoids that are apparently nearly devoid of all matter. Thesevoid typically have diameters around 140-170Mpc (taking H=70km/sec/Mpc) and occur with some regularity ... These vast structurespose acute problems for the Big Bang theory, for there simply is notenough time to form them in the hypothesized 14 Gy since the BigBang, given the observed velocities of galaxies in the present-dayuniverse. Measurements of the large scale bulk streaming velocitiesof galaxies indicate average velocities around 200-250 km/sec ... theproduction of the large voids observed requires three to six times asmuch time as that allowed by the Big Bang theory. ... An explosivemechanism that rapidly injects energy into the medium could formvoids more rapidly than gravitational attraction. ... The plasmacosmology approach can, however, easily accommodate large scalestructures, and in fact firmly predicts a fractal distribution ofmatter with density being inversely proportional to the distance ofseparation of objects ... This relation flows naturally from thenecessity for collapsed objects to be collisional, and from the scaleinvariance of the critical velocities of magnetic vortex filaments,which are crucial to gravitational collapse. This fractal scalingrelationship (fractal dimension=2) has been borne out by many studieson all observable scales of the universe ... In the plasma model,where superlcusers, clusters and galaxies are formed frommagnetically confined plasma vortex filaments, a break in the scalingrelationship is only anticipated at scales greater than approximately3Gpc. ...

.. The plasma alternative views the energy for the CBR asprovided by the radiation released by early generations of stars inthe course of producing the observed 4He. The energy is thermalizedand isotropized by a thicket of dense, magnetically confined plasmafilaments that pervade the intergalactic medium. While this modelhas not been developed to the point of making detailed predictions ofthe angular spectrum of the CBR anisotropy, it has accurately matchedthe spectrum of the CBR using the best-quality data set from COBE ...Since this theory hypotheses filaments that efficiently scatterradiation longer than about 100 microns, it predicts that radiationlonger than this from distant sources will be absorbed, or to be moreprecise scattered, and thus will decrease more rapidly with distancethan radiation shorter than 100 microns. ...

... The WMAP resultscontradict the Big Bang theory and support the plasma cosmologytheory in another extremely important respect. Tegmark et al ... haveshown that the quadrupleand octopole component of the CBR are not random, but have a strongpreferred orientation in the sky. The quadruple and octopolepower is concentrated on a ring around the sky and are essentiallyzero along a preferred axis. The direction of this axis isidentical with the direction toward the Virgo cluster and liesexactly along the axis of the Local Supercluster filament of whichour Galaxy is a part. This observation completely contradicts theBig Bang assumption that the CBR originated far from the localSupercluster and is, on the largest scale, isotropic without apreferred direction in space. ... the plasma explanation is farsimpler. If the density of the absorbing filaments follows theoverall density of matter, as assumed by this theory, then the degreeof absorption should be higher locally in the direction along theaxis of the (roughly cylindrical) Local Supercluster and lower atright angles to this axis, where less high-density matter isencountered. This in turn means that concentrations of the filamentsoutside the Local Supercluster, which slightly enhances CBR power,will be more obscured in the direction along the supercluster axisand less obscured at right angle to this axis, as observed. More workwill be needed to estimate the magnitude of this effect, but it is inqualitative agreement with the new observations. ...".

According to astro-ph/0008212,by Tatsuno, Berezhiani, and Mahajan. "...the interaction of largeamplitude electromagnetic waves with a hot electron-positron (e-p)plasma (a principal constituent of the universe in the MeV epoch)leads to a bunching of mass, energy, and angular momentum in stable,long-lived structures. Electromagnetism in the MeVepoch, then, could provide a possible route for seeding the observedlarge-scale structure of the universe. ...".

Kaplinghat,Steigman, Tkachev, and Walker, in astro-ph/9805114, say: "...

The present age/expansion rate (Hubble parameter) constraint ...and the SN Ia magnitude-redshift relation require ... alpha > 0.6... , while production of primordial helium and deuterium force alphato be smaller. ...". Since a single power-law expansion for all agesof our universe would either produce a universe that is too young ora universe in which the temperature does not drop below the 80 keVthreshhold for nucleosynthesis prior to neutron decay, a single powerlaw expansion is not consistent with both the age of our universe andthe standard model of Big Bang Nucleosynthesis.

In particular, their paper indicates that the linearly (alpha = 1) expanding universe models of

which were models that I had formely found very attractive and had described favorably on earlier versions of my web pages, are probably not accurate models of our universe.

With respect to the standard cosmological model of a RadiationEra, in which the scale of the universe expands as t^1/2, followed bya Matter Era, in which the scale of the universe expands as t^2/3,their paper is consistent with it being an accurate model of ouruniverse, as is indicated by the red line (with two slopes, changingat the Radiation/Matter Era boundary) on my modification of Fig. 1 oftheir paper.

   At about T = 1 eV or about 10^3 to 10^4 degK the density of matter has exceeded the density of radiation;photons decouple and the sky is transparent; matter recombines into atoms; a residual ionization freezes in. According to Peebles, at decoupling the redshift z = 1400. 

As Weinberg (1988) says, "... It is striking that the transitionfrom a radiation- to a matter-dominated universe occurred at justabout the same time that the contents of the universe were becomingtransparent to radiation, at about 3,000 degrees K. ... We also donot really know which transition occurred first. ...".

According to Narlikar and Padmanabhan (1986) section 8.4.2, Weinberg (1972), and Weinberg (1988):  Just after recombination, the Jeans mass was 1.6 x 10^5 Msun, which is the mass of globular clusters.  Just before recombination, the Jeans mass was 5 x 10^18 Msun, which is the mass of a large cluster of galaxies.  

For example, if the typical galaxy has mass 10^11 Msun, and ifgalaxies are about a million light years apart, then 5 x 10 ^18 Msunwould be 50,000,000 galaxies. Since the cube root of 50,000,000 isabout 370, the cluster size would be about 370 million light yearsacross, which is consistent with the 300 million light year size ofGalactic Clusters observed when Subir Sakar did a computer analysisof data from the Anglo-Australian Automatic Plate Measuring suvey(New Scientist article by Marcus Chown, 25 April 1998, page 7).

Since electromagnetic processes may well have been interesting atthe time of formation of atoms and decoupling of photons, thestructure formation problem may be solved

by magnetic structures in theRadiation Era of the universe at or prior to recombination,


by the Layzer mechanism of structure formationin a cold universe, as applied to the component of the universeconsisting of cold Planck mass black holes.

	In the future, when the open Robertson-Walker universehas expanded enough to become very dilute,it may be enough like the original flat Minkowskian vacuumto repeat the quantum conformal fluctuation process.(Gunzig, Geheniau, and Prigogine (1987))      Processes of universe-creation are described by Gott and Li in their paper Can the Universe Create Itself?    


and Layzer Process ofStructure Formation with Cold BlackHoles:

  Battaner, in astro-ph/9801276, and Battaner and Florido, in astro-ph/9802009, have described a set of nested egg-carton structures using the Octonionic structure of nested Onarhedral lattices, In their model, very large-scale magnetic fields may have played a very important role in building up the present large-scale structure of the Universe, particularly at the MeV Era of evolution of our universe. 

In 1997 Charles Steidel of Caltech (Science276 (4 April 1997) 36) observed walls of galaxies hundreds ofmillions of light years long at redshifts between 2.8 and 3.5, only 2billion years after the Big Bang.

In 2001, a 22 May BBCarticleby David Whitehouse reported that "... New observations aresupporting recent computer models that suggest the early Universe was"spongy",

with galaxies forming along filaments,like droplets on a spider's web. ... recent computer simulationsof the early Universe have one prediction in common: the firstlarge-scale structures to form were long filaments connected at theirends by "nodes". The models typically look like a three-dimensionalspider's web, or perhaps the neuronalstructure of a brain. ... Itis believed that the first galaxies would have formed inside thethreads of the web. When they started emitting light, they would havebeen seen to mark out the otherwise invisible threads, much likebeads on a string. In the course of millions and billions of years,those early galaxies would stream along these threads, towards andinto the "nodes". This is where galaxy clusters would be formedlater. ... observations, with the European Southern Observatory's(ESO) Very Large Telescope at Paranal, of a region around a quasar,whose light set off when the Universe was only 15% of its presentage, have now identified a string of galaxies that map out a tightfilament in the early Universe. ...

... One of the researchers involved, Palle Moller ... said. "Atthis enormous distance, we see it at a time when the Universe wasonly about two billion years old. This is obviously in agreement withthe predictions by the computer models of a web-like structure ..."....".


A rough redshift timetable for variousstructures

(mostly based on Peebles (1993)) is:
Layzer's model needs no pre-existing perturbation anisotropy to form such structures.	In the cold universe model of Layzer, there is cluster formation on all scales and the clustering process continues forever. 	Although Layzer bases his cold universe model on hydrogen,it should be possible to base such a model on Planck-massblack holes as the cold dark matter in a manner consistentwith the D4-D5-E6-E7-E8 VoDou Physics model.Another possibility for at least some dark matter is gravitational interaction from other Worlds of the Many-Worlds.	Particle Creation in the Inflationary Universe should be such that any inhomogeneity can be contained in a spherical region within which the average density of mass is the same as the average density of the entire universe.	At all times during the expansion of the universe, the cold dark Planck mass black holes constitutea critical point gas, and therefore unstable againstfluctuations on all scales, particularly unstable againstdensity fluctuations on the scale of the entire universe at that time  (Layzer (1984)).  The result is structure formation at all scales.  	Layzer's model begins with the Clausius equation 		2K + (B - 1)U = 3PV , where K=kinetic energy, U=potential energy, P=pressure,V=volume, and B=2 for gravity, with an inverse square force law.In adiabatic expansion,d(K + U)/ dt  +  P  dV/dt  =  0. Then: d(K + U)/dt  +  (1/3) ((2K + U) / V)  dV/dt  =  0. If V is proportional to  a^3, where a(t) is the cosmic scale factor,then (1/V) dV/dt = (1/a^3) da^3/dt = 3a'/a = 3H so that d(K + U)/dt + H(2K + U) = 0  	Let U = SUM(i,j)  -(1/2) G m'_i m'_j / r_ij  , whereG is Newton's constant, m'_i is the excess mass in a cell ofvolume dV_i, and r_ij is the distance between cell i and cell j.Let  p" be  the mean density,A = {p - p"} / p"  be the relative amplitude of density fluctuations,and L be the average scale of density variations. 	Then, consider V to be a spherical region enough larger thanthe size L^3 that any fluctuations inside V can be consideredto be contained entirely within V.  In particular, the part ofthe universe outside V can then be considered to be ofuniform density and its gravitational influenceinside V can be ignored.	Then  U = SUM(i,j)  -(1/2) G m'_i m'_j / r_ij  =                  =  -2 pi G p" A L^2  p" Vbecause  INT(theta) INT(phi) INT(r) = 4 pi INT(r) ,SUM(i in V) m'i = SUM(i in V) {p - p"} dVi  == SUM(i in V) p" A Vi =  p" A L£ , {r_ij} = L ,  and   SUM(j in V) dVj = V . 	If O is the temperature and N is the number of particles, P = (2K+U) / 3V = (N O / V) - (2 pi / 3) G A p"^2 L^2 . 	Now assume that V is such that, if V is compressed by dV,p" V remains constant, A = {p - p"} / p"  remains constant,and L =prop= V^(1/3).Then dV/V  =  -dp"/p"  =  3dL/L  and dA = 0 , and dP = ( (N O / V) - (4/3)(2 pi /3) G A p" L^2 )(-dV/V) == (P - (1/9) 2 pi G A p"^2 L^2) (-dV/V)  	Layzer's model is based on the expanding universe being like avapor at its critical point, dP = 0, unstable against the growthof fluctuations at all scales.	This requires a cold universe, so that |K| { |U| while 2K+U } 0.	Sinced(K + U)/dt + H(2K + U) = 0 if K+U is negative and 2K+U is positive, expansion causes K+Uto decrease further, so that the magnitude of the (negative)potential energy U increases still further.  If the magnitudeof U increases enough so that 2K+U becomes negative,K+U increases.	Physically, the increase of the magnitude of the potentialenergy U  causes clusters of clumps of matter to form. The clumps within a cluster are accelerated by the fluctuatinggravitational field due to the increase in the magnitude ofthe potential energy U.  The motion of the clumps then increasesthe kinetic energy K and the pressure, quenching the instability. 	The processes act to keep the cold universe in its critical state,in which  2K+U = 0 and dP = 0.	The critical value for the pressure, Pcrit, at dP = 0 , isPcrit = (1/9) 2 pi G A p"^2 L^2.The total energy at Pcrit is  E = K+U = U/3.	Then:		K =prop= a(t) ; U =prop= a(t) ; and E =prop= a(t) . 	The size of the clumps is of the scale L =prop= a^2 ,because p"V is constant in time, p" =prop= a^(-3),U =prop= a, A is constant, and U = -2 pi G p" A L^2 p V. 	The mass M of clumps is proportional to p" L^3,so that M =prop= a^3. 	In the expanding universe, a heirarchy of larger and largerself-gravitating clusters forms, with the self-gravitatingclusters of one stage forming the clumps in the clustersof the next stage. 	The diameter of the clusters is L =prop= M^(2/3). 	Layzer estimates that at the onset of instability againstformation of self-gravitating clusters of clumps of matter,the relative amplitude of density fluctuations A = {p - p"} / p"  is of the order 1/10 to 1/100.	The energy per unit mass e of the cluster is given bye = (K+U) / p"V = (-(2/3)U + U) / p"V == U / 3 p" V = (1/3)(-2 pi) p" A L^2 G .	Since p" =prop= 1/V =prop= a^(-3) and L^2 =prop= a^4 :e =prop= a =prop= M^(1/3).	Layzer notes that the relationship e =prop= M^(1/3) isconsistent with observation from the scale of Jupiter andits satellites to the scale of clusters of galaxies. 	The clusters of clumps of matter are of the scale of volumeV =prop= a^3, while the clumps of matter within self-gravitating cluster are of the scale ofvolume L^3 =prop= (a^2)^3 = a^6. Therefore, at some time after the beginning of theFriedman Robertson-Walker expansion,L will grow large enough to equal V.So, on very large scales, larger than clusters of galaxies,structures are formed after the universe has expanded enoughso that the clumps are so large that they will not all fallas spherical units into a cluster in the potential wellsof the Layzer process, but some will be stretched andpulled among nearby clusters, thus forming luminousfilaments and sheets as well as voids. 

Mass Distribution in Galaxies:

 	Consider the stage of the Layzer clustering heirarchy atwhich the self-gravitating clusters are the size of glaxies.The galactic-size cluster should be a self-gravitatingspherical region that is gravitationally dominated bycold dark Planck mass black holes.Since the Planck mass black holes have very small(10^(-66) cm^2) cross section, they can be considered to becollisionless within the cluster.	The cluster of dark matter can be considered to be anisothermal ideal gas of pressure pr, density p, andequation of state pr =prop= p.As it is self-gravitating, its equation of hydrostatic support is	dpr/dr = (kT/m) dp/dr = -p GM(r) / r^2  ,where k is Boltzmann's constant, T is temperature, andm is the Planck mass of the black hole, or	d (r^2 dlnp)/dr) /dr  =  -(Gm/kT) 4pi r^2 p  ,which is equivalent to a collisionless systemwith distribution function	(p_1/(2 pi kT/m)^(3/2)) exp((F - (1/2)V^2) / (kT/m)) ,which gives	p = p_1 exp(F / (kT/m))as shown in sectiion 4.4.3(b) of Binney and Tremaine (1987).As they show, a nonsingular solution for this isothermalsphere is given by	d (r'^2 dlnp'/dr') /dr'  =  -9 r'^2  p'where p' = p/p_0 ,  r' = r/r_0 , and r_0 = Sqrt(9 kT / m 4 pi G p_0)is the core radius.	At r { 2 r_0 ,  p'(r') = 1/(1 + r'^2)^(3/2)   , correct to about 5%.	At  r } 15 r_0 ,  p'(r') = (2/9) r'^(-2)  , andthe nonsingular isothermal sphere solution approachesthe singular isothermal sphere solutionp(r) = kT / m 2 pi G r^2 .	The circular speed Vc at r is Vc^2  = G M(r) / r  ,where M(r) is the mass inside a sphere of radius r.	From      d (r^2 dlnp/dr) /dr  =  -(Gm/kT) 4 pi r^2 p  ,Vc^2  =  -(kT/m) dlnp / dlnr .	The circular speed Vc curve for the nonsingular isothermalsphere is similar to observed galactic rotation curves(figure 4-8, figure 10-1, and figure 10-2 of Binney and Tremaine (1987)).In section 10.1.6, Binney and Tremaine (1987) state that thedensity distribution of a dark halo that would give the observedflat rotation curves at large r"is also the density distribution for the isothermal sphere at large radii ... .However, there is no compelling theoretical argument to suggestwhy the dark halo should resemble an isothermal sphere." 	I disagree:  Layzer clustering of cold dark Planck massblack holes is such a compelling theoretical argument. 	Binney and Tremaine (1987, section 4.4.3(b)) state"From the astrophysical point of view, the isothermal spherehas a very serious defect:  its mass is infinite.  Thus fromequations 4-127 and Figure 4-7, we have thatM = 2 s^2 r / G [s^2 = kT / m] at large r.Clearly no real astrophysical system can be modeled overmore than a limited range of radii with a divergent mass distribution.On the other hand, the rotations curves of spiral galaxies(section 10.1.6 and MB section 8-3) are  often remarkably flat out to great radii, and this suggests that we try to construct models that deviate from the isothermal sphere only far from their cores."  	I disagree with the statement that the isothermal sphere mass distribution is a defect.  

Dennis Zaritsky, in astro-ph/9810069,"... collate[s] published results and demonstrate[s]that they are all consistent with a Galactic halo that is nearlyisothermal with a characteristic velocity of 180 to 220 km/sec and anextent greater than or equal to 200 kpc. ... All of the data ... areentirely consistent with an isothermal sphere... . There is noevidence for a significant truncation of the mass profile at largeradii. ..."


The critical density sufficient to make Omega = 1 is about 1.88 x 10^(-29) h^2 gm/cm^3 (Kolb and Turner (1990)).  The galactic rotation curve halo density is on the order of at least (it could be about an order of magnitude greater) 0.01 Msun/pc^3 (Binney and Tremaine (1987), section 10.1.6), or about 0.01 x 2 x 10^33 / (3 x 10^18)^3 = = .0007 x 10^(-21) = 7 x 10^(-25) gm/cm^3.	The minimum rotation curve halo density is therefore at least about 3 x 10^4 times greater than the Omega = 1 critical density.  In the Layzer clustering model, the isothermal sphere density p at large r varies as    p =prop= 1 / r^2.  In it, p at r = 3 r_0 = 10 kpc (roughly the 8.5 kpc distance from the sun to the center of our galaxy) is 4 x 10^4 times greater than p at r = 600 r_0 = 2 Mpc (the median radius of clusters of galaxies is about 3 h^(-1) Mpc (Binney and Tremaine (1987), table 1-4)). 	As a lot of the mass in the universe may be in cold dark matter, Layzer's model should describe structure formation on scales large enough that gravity is the dominant force (structures at planetary scale or larger).   	On smaller scales, where electromagnetism or other forces are stronger, the cold dark matter (being very weakly interacting with respect to forces other than gravity) should be ignored or considered as a background, with the standard hot big bang model applying to the small scale processes.  	Except for gravitational interaction, the cold dark matter would be decoupled from the hot ordinary matter and radiation at all times after the end of inflation.  The radiation would decouple from the ordinary matter about 200,000 years after the end of inflation.	Structure in the Layzer process is always subhorizon in size, so that anisotropy of the microwave background is small-angular scale, O much less than 1 deg = decoupling Hubble scale (Kolb and Turner (1990), section 9.6.2), and not measurable by COBE. 	With two classes of matter (cold dark matter forming structure according to Layzer's theory and ordinary matter having a lesser role to play on gravitational scales because it is much less massive), the fact that the ordinary Jeans mass after decoupling is about the mass of a globular cluster indicates an ordinary process of globular cluster formation within the structures already formed at that time by Layzer's cold matter process. de Vega, Sanchez, and Combes suggest that the fractal structure of the InterStellar Medium of our galaxy, on scales from about 20 AU to about 300 light-years, may be due to self-gravity of isothermal clouds, rather than cascades of turbulence due to galactic rotation. Shear of galactic rotation destroys fractal structure above 300 light-years in size, and stellar radiation destroys fractal structure below 20 AU and in regions of dense stellar formation and/or radiation.  


 Binney, J. and Tremaine, S. (1987), Galactic Dynamics   (Princeton, Princeton). Dolgov, A. (1980), Sov. Phys. JETP  52, 169. Gott, J. R. (1982, 28 January), Nature 295, 304.	Gunzig, E., Geheniau, J., and Prigogine, I. (1987), Nature  330, 621. Kolb, E., and Turner, M. (1988), The Early Universe:  Reprints  (Addison-Wesley, Redwood City, Calif.). Kolb, E., and Turner, M. (1990), The Early Universe  (Addison-Wesley, Redwood City, Calif.). Kugo, T., and Townsend, P. (1983), Nuc. Phys.  B221, 357. Lawson, H., and Michelsohn, M.-L. (1989), Spin Geometry  (Princeton, Princeton). Layzer, D. (1984), Constructing the Universe  (Freeman, N.Y.). Linde, A. (1984), Rep. Prog. Phys.  47, 925. MacGibbon, J. (1987), Nature  329, 308. Narlikar, J., and Padmanabhan, T. (1986), Gravity, Gauge Theories and Quantum Cosmology  (Reidel, Boston) Peebles, P. J. E. (1993), Principles of Physical Cosmology (Princeton, Princeton).  Taubes, G. (1994, 25 March), Science 263, 1682, 1683.   Weinberg, S. (1972), Gravitation and Cosmology (Wiley, New York). Weinberg, S. (1988), The First Three Minutes (Basic books). Weinberg, S. (1989), Rev. Mod. Phys.  61, 1.   

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